1. Field of the Invention
The present invention is directed to a method and apparatus for separating ions of differing charge-to-mass ratio and more particularly to a method and apparatus of separating ions of differing charge-to-mass ratio utilizing the principle of the stability of orbital motion of an ion in certain magnetic field configurations.
2. Description of the Prior Art
The propagation of a relativistic electron beam in a transverse periodic magnetic structure is known. In the study of the electron beams in magnetic fields in a free electron laser, the most frequently used periodic magnetic field is the transverse field produced on the axis of a double helical current winding with equal and opposite currents in each helix. Such a device is usually referred to as a magnetic wiggler. The unperturbed motion of the electrons of the beam in the wiggler is quite simple. The reason for simplicity is that the magnetic field on the axis of a wiggler can be approximately described by a transverse vector potential A.sub..perp. (z), depending only on the distance z along the axis. Therefore, the canonical transverse momentum EQU P.sub..perp. =.gamma.mv.sub..perp. -(e/c)A.sub..perp. ( 1)
of an electron is a constant of motion, which with the conservation of energy EQU .gamma.=[1-(v.sub..perp. /c).sup.2 -(v.sub.z /c).sup.2 ].sup.-1/2 =const, (2)
uniquely defines the perpendicular and parallel components v.sub..perp. and v.sub.z of the velocity of the electrons in the beam for a given assignment of A.sub..perp. (z). The electrons in the magnetic wiggler have helical trajectories with the same period as that of the wiggler.
The magnetic field produced by the wiggler can be described by the equations EQU B=.gradient..times.A.sub..perp., where (3) EQU A.sub..perp. A.sub..perp. (z) [e.sub.x cos k(z)z-ey.sub. sin k(z) z], (4)
where k(z) is the slowly varying wavenumber of the wiggler field.
If an axial magnetic field B.sub.o (z) has been added, it can alter dramtically the orbit as compared to the orbit in a wiggler without B.sub.o (z). For A.sub..perp. and k independent of z, the vector potential in equation (4) describes the field on the axis of an infinite magnetic wiggler, where, as is well-known. EQU A.sub..perp. =I[ak K.sub.o (ak)+K.sub.1 (ak)], (5)
where I is the current in the wiggler, a is its radius, ##EQU1## .lambda. is the pitch of the winding of the wiggler, and K.sub.o and K.sub.1 are the modified Bessel functions of the second kind. By using the more general form of equation (4) for the vector potential, slow variations of the wiggler parameters a and k with z can be obtained, and the magnitude A.sub..perp. (z) in equation (4) can be approximated by equation (5), where a and k correspond to the values of these parameters in the non-uniform wiggler at point z.
Although the magnetic field represented by the potential (4) does not satisfy .sup..gradient. .times.B=0, it gives a good approximation of the exact curl-free field on an infinite wiggler at small distances r from its axis.
The electron beam dynamics are described in more detail in Friedland, "Electron Beam Dynamics in Combined Guide and Pump Magnetic Fields for Free Electron Laser Applications"; Physics Fluids, Volume 23, Number 12, December 1980; pages 2376-2382; said article being incorporated herein by reference.
Although the dynamics of electron beams in magnetic fields generated by a wiggler have been studied, the application of the physical principles involved has not been extended to other ionized particles of matter. Further, the application of the principles involved to the separation of ionized particles having different charge-to-mass ratios has not been studied heretofor.